Angular frequency: The frequency of a wave measures the number of times a complete wave cycle will pass a given position. Angular frequency is similar, except that it's been converted to a form that's easier to use in trigonometric equations. While frequency measures cycles per second, or Hertz, angular frequency measures radians per second, where radians are a measurement of an angle similar to degrees. There are 2Ï radians in a circle, so a frequency of 1 Hertz is equivalent to an angular frequency of 2Ï.
emf and potential difference are 2 different quantities whose magnitude may be equal in certain conditions. The emf is the work done per unit charge by the battery force which is non-electrostatic in nature. The potential difference originates from electrostatic field created by the charges accumulated on the terminals of the battery.The emf of a battery equals to potential difference between its terminals when the terminals are not connected externally.
if r = internal resistance of a battery and i = current , E = emf, then
potential difference V = E - iR ( R = resistance )
Hope this helps.